A097786 a(n) = 3*a(n-1) + C(n+3,3) for n > 0; a(0)=1.

1, 7, 31, 113, 374, 1178, 3618, 10974, 33087, 99481, 298729, 896551, 2690108, 8070884, 24213332, 72640812, 217923405, 653771355, 1961315395, 5883947725, 17651844946, 52955536862, 158866612886, 476599841258, 1429799526699

Offset

0,2

Comments

Partial sums of A052150.

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).

Formula

G.f.: 1/((1-3*x)*(1-x)^4);

a(n) = 3^(n+4)/16 - (4*n^3 + 42*n^2 + 152*n + 195)/48;

a(n) = Sum_{k=0..n} binomial(n+4, k+4)*2^k.

a(n) = 7*a(n-1) - 18*a(n-2) + 22*a(n-3) - 13*a(n-4) + 3*a(n-5); a(0) = 1, a(1)=7, a(2)=31, a(3)=113, a(4)=374. - Harvey P. Dale, Nov 26 2011

Mathematica

RecurrenceTable[{a[0]==1, a[n]==3a[n-1]+Binomial[n+3, 3]}, a, {n, 30}] (* or *) LinearRecurrence[{7, -18, 22, -13, 3}, {1, 7, 31, 113, 374}, 31] (* Harvey P. Dale, Nov 26 2011 *)

Crossrefs

Sequence in context: A109756 A055580 A364635 * A350498 A197649 A006458

Adjacent sequences: A097783 A097784 A097785 * A097787 A097788 A097789

Keyword

easy,nonn

Author

Paul Barry, Aug 24 2004

Status

approved